# Chemistry and the Scientific Method | General Chemistry 1

## Scientific Notation

Scientific notation is a way of writing a very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

850,000,000 = 8.5 x 10

^{8}in scientific notation

0.0000023 = 2.3 x 10^{-6 }in scientific notation

## The Metric System of Units and Standards

The preferred system of units used in scientific work is the metric system.

We express all measurements in terms of one set of metric units called SI units.

Basic SI units:

- length ⇒ meter = m

- mass ⇒ kilogram = kg

- temperature ⇒ kelvin = K

- time ⇒ second = s

- amount of substance ⇒ mole = mol

In the metric system, the designations of multiples and subdivisions of any unit can be obtained by adding a prefix to the name of the unit.

Common prefixes for SI units:

giga- (= G) ⇒ 10^{9}

mega- (= M) ⇒ 10^{6}

kilo- (= k) ⇒ 10^{3}

centi- (= c) ⇒ 10^{-2}

milli- (= m) ⇒ 10^{-3}

micro- (= m) ⇒ 10^{-6}

nano- (= n) ⇒ 10^{-9}

pico- (= p) ⇒ 10^{-12}

femto- (= f) ⇒ 10^{-15}

Volume (V): SI unit is m^{3}.

A more convenient measure of volume is the liter:

1L = 1000 cm^{3} = 1 dm^{3 }and 1 m^{3} = 1000 L

Temperature (T): SI unit is K.

However, there are 3 different temperature scales in common use: the Celsius scale, the Fahrenheit scale and the Kelvin scale.

T (in K) = T (in °C) + 273.15

T (in °C) = (5/9) x [T (in °F) – 32.0]

Density (d): SI unit is kg.m^{-3}.

Density is defined as the mass per unit volume of a substance: d = m / V.

## Intensive vs. Extensive Properties

Intensive properties: properties independent of the amount of a substance.

Ex: density, color, temperature, hardness, melting point

Extensive properties: properties directly proportional to the amount of a substance.

Ex: masse, volume, weight, length

## Energy and Power in Chemistry

Energy (E): SI unit is the joule (J).

It can be defined as the ability to cause a change in a physical system.

Kinetic Energy (E_{k}): energy associated with a moving object

E_{k} = $\frac{1}{2}$ mv^{2}

m =mass of the object (in kg)

v = velocity of the object (in m.s^{-1})

Potential Energy (E_{p}): energy of an object due to its location relative to a reference point.

If the ground is the reference point:

E_{p} = mgh

m = mass (in kg)

g = the gravitational acceleration constant = 9.81 m.s^{-2} (on Earth)

h = the height (in m)

Law of conservation of energy: E_{total} = E_{k} + E_{p} = constant

Power: SI unit is a watt (W) = J.s^{-1}.

It can be defined as the rate at which energy is produced or utilized.

## Accuracy vs. Precision

Accuracy: refers to how close our measurement/result is to the actual value.

Precision: refers to how well repeated measurements give the same results and how sensitive a measuring instrument was used.

Percentage error can be used to measure accuracy:

% error = $\left|\frac{\mathrm{average}\mathrm{value}-\mathrm{true}\mathrm{value}}{\mathrm{true}\mathrm{value}}\right|\times 100$

## Number of Significant Figures

The precision of a measured quantity is indicated by the number of significant figures.

Rules for determining the significant figures:

- Non-zero digits are always significant

- any zeros between two significant digits are significant

- Final zeros in the decimal portion only are significant

0.0

51has 2 significant figures

0.0510has 3 significant figures

5.100x 10^{3}has 4 significant figures

Numbers that can be counted exactly are considered exact numbers. They have no limit to their precision (may be treated as having an infinite number of significant figures).

10 persons in a room = exact number = infinite number of significant figures

## Calculated Numerical Results

Calculated numerical results should show the correct number of significant figures.

For addition and substraction:

- Count the number of significant figures in the decimal portion of each number

- Add or substract in the normal fashion

- The final answer may have no more significant figures to the right of the decimal than the least number of significant figures in any number in the exercise.

5.05 – 3.229 = 1.82

For multiplication and division:

Number of significant figures of the final answer = The least number of significant figures in any number of the exercise.

2.1 x 0.0568 = 0.12

## Dimensional Analysis

Dimensional Analysis = method to convert one different type of unit to another, but the value of the quantity stays the same. To do this, we use a conversion factor which is the relationship between two units.

Convert 2 hours in minutes:

The dimensional analysis is $\frac{60\mathrm{minutes}}{1\mathrm{hour}}$

⇒ the conversion factor is 60So 2 hours in minutes : 2 hours x $\frac{60\mathrm{minutes}}{1\mathrm{hour}}$ = 120 minutes

Convert 50 miles.hour

^{-1}in m.s^{-1}:

50 miles.hour

^{-1}= $\frac{50\mathrm{miles}}{1\mathrm{hour}}$ x $\frac{1.61\mathrm{km}}{1\mathrm{mile}}$ x $\frac{1000\mathrm{m}}{1\mathrm{km}}$ x $\frac{1\mathrm{hour}}{60\mathrm{min}}$ x $\frac{1\mathrm{min}}{60\mathrm{s}}$50 miles.hour

^{-1}= $\frac{50\times 1.61\times 1000}{60\times 60}$ m.s^{-1}= 22.4 m.s^{-1}